Question 1: Given fuzzy set A, describing pressure p is higher than 15 mPa, through the membership function: 1 (x) x> 15, 1+ (x-15) -0 x ≤ 15, and fuzzy set B, describing pressure p is approximately equal to 17 mPa, with membership function: H8(x) 1+(x-17) Find the membership function of the fuzzy set C, describing pressure p is higher than 15 mPa and approximately equal to 17 mPa. draw membership functions. Note: Use Computer Software Question 2: Consider the membership functions of fuzzy sets A and B. Evaluate μA-B(x, y), using Zadeh implication, and plot in MATLAB. HA(x) = max {0, 10x-3) 0.3≤x≤0.5 2 ax {0.7-10x) 0.5<x≤0.7 max 0, 2 =0 otherwise He(y) = max {0. 10y-3) 0.3 sy≤0.5 =0 2 nax {0. 7-10v } 0, 0.5 <y≤ 0.7 otherwise Question 3: Use MATLAB Fuzzy-logic toolbox to solve example 6.3 (Two-input fuzzy controller for level control) [given in the lecture slides]. Define the membership functions for inputs-outputs and the rules as given in the example. Assume that the error introduced is as given below: (1.25t-2.5,0 st≤7 e(t)=-5.4t+44,8 st≤ 10 For the evaluation of control rules use: (i) Mamdani min implication and min interpretation of AND (DOF), (ii) Larsen product implication and min DOF, (iii) Larsen product implication and product DOF. Compare the three methods for u* values at t = 4 and 9 minutes. Fill out the tables with the following defuzzification methods: u* at t=4min (i) Mamdani with min DOF (ii) Larsen with min DOF (iii) Larsen with product DOF u* at t=9min (i) Mamdani with min DOF (ii) Larsen with min DOF Centroid Bisection MOM Centroid Bisection MOM (iii) Larsen with product DOF Additionally, for case (i) i.e. Mamdani with min DOF and centroid method of defuzzification: (a) Plot the control hypersurface. (b) Plot u for time range of t = 0 to 10 minutes, assuming a sampling time of t=0.1 seconds. Hint: After you develop your fuzzy structure (.fis file), you can use evalfis function in MATLAB, and provide e and Ae input to it to evaluate u for a number of input values. Submit the Word document of the report along with fis (fuzzy logic matlab file)